As described in many texts on the subject of optics (for example, M. Klein, Optics, John Wiley & Sons, Inc., New York, 1986, pp. 193–256, incorporated herein by reference) lenses produce non-uniform exposure at the focal plane when imaging a uniformly illuminated surface. When the lens is modeled as a thin lens, the ratio of the intensity of the light of the image at any point is described as cos4 of the angle between the optical axis, the lens, and the point in the image plane. This cos4 falloff does not include such factors as vignetting, which is a property describing the loss of light rays passing through an optical system.
In photographic images, this cos4 falloff generally causes the corners of an image to be darker than desired. The effect of the falloff is more severe for cameras or capture devices with a short focal length lens. In addition, flash photography will often produce an effect similar to falloff if the subject is centrally located with respect to the image. This effect is referred to as flash falloff.
As described in U.S. Pat. No. 5,461,440 (incorporated herein by reference), it is commonly known that lens falloff may be corrected by applying an additive mask to an image in a log domain or a multiplicative mask to an image in the linear domain. This conventional cos4 based mask is solely dependent upon a single parameter: the focal length of the imaging system. Also, images with flash falloff in addition to lens falloff may by compensated for by a stronger mask (i.e. a mask generated by using a smaller value for the focal length than one would normally use.)
Toyoda and Yamasaki describe in U.S. Pat. No. 5,461,440 (incorporated herein by reference) a method of recording a camera identification code onto the film upon which an image is captured. This identification code specifies lens information that may be used at the time the image is processed to select an appropriate level of falloff compensation. However, it is not always practical or possible to record such information onto photographic film. Additionally, many scene dependent factors affect the apparent level of light falloff present in a scene, including exposure level (extremely underexposed scenes never appear to contain falloff), flash condition, and scene geometry.
Gallagher and Gindele (in U.S. Pat. No. 6,670,988, issued on Dec. 30, 2003 and incorporated herein by reference) describe a variety of other methods of selecting the parameter used to generate the falloff compensation mask. For example, in this conventional teaching the parameter could be selected in order to simulate the level of falloff compensation that is naturally performed by the lens of the optical printer. Additionally, the parameter could be determined interactively by an operator using a graphical user interface (GUI) or, the parameter could be dependent upon the film format (APS or SUC) or the sensor size. Finally, they teach a simple automatic method of determining the parameter. A selected set of low resolution frames are averaged to generate an analysis frame. A cos4 surface model is fit to this analysis frame. This value of the parameter f used to fit the cos4 model to the analysis frame is determined to be the value of the parameter f for generating the falloff compensation mask for the selected set of images. However, with such a system, an image of a person with a white shirt standing in front of a gray wall would be interpreted as a great deal of falloff because the image would have darker edges relative to the image center.